It's on the outskirts. Since the outside part of a city has no borders, the correct preposition to use is on.
It's "on the outskirts". Since the outside part of a town or city has no borders, the correct preposition to use is "on".
The airport is located on the outskirts of Bangkok.
Remember, "in" is a preposition that indicates that something is located inside or within an area. Because the outskirts have no borders, it makes more sense to say "on the outskirts" than "in them".
Olga lives on the outskirts of Moscow.
This graph illustrates that the prepositional phrase "on the outskirts" is more commonly used than "in the outskirts".
Source: Google Books Ngram Viewer
A suburb, by contrast, is a residential area with a border around it. You can be in it, and therefore say "in the suburb". This is the main difference between outskirts and suburbs.
He grew up in the suburbs of the city.
He used to play on the outskirts of the city.
Being a plural noun, we cannot use the article a/an before outskirts. Be also aware that it requires a plural form of a verb, so we say "outskirts have" (not "outskirts has").
